The magnetic properties of the mixed spin-1 and spin-5/2 Ising system with a crystal-field interaction in the presence of a time-varying oscillating external magnetic field on a hexagonal lattice are studied using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins sigma = 1 and S=5/2. The set of mean-field dynamic equations is obtained by employing the Master equation. These equations are solved and firstly, the time variations of the average sublattice magnetizations are investigated in order to find the phases in the system. Then, the thermal behaviors of the dynamic sublattice magnetizations and the dynamic total magnetization are also investigated to obtain the dynamic phase transition points and the dynamic compensation temperatures. From this investigation, the nature (continuous and discontinuous) of the phase transitions and the type of the compensation behavior are determined. The dynamic phase diagrams are presented for both the presence and absence of the dynamic compensation temperatures in the nine different planes. It was found that the system exhibits five fundamental phases, nine different mixed phases which are composed of binary and ternary combinations of fundamental phases and the compensation temperature or the N-type behavior in the Neel classification nomenclature. (C) 2012 Elsevier B.V. All rights reserved.